{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "60e1be86",
   "metadata": {},
   "source": [
    "# Laplace Transform\n",
    "\n",
    "$$\n",
    "F(s) = \\int_0^\\infty f(t)e^{-st}dt \\tag{1}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b908df5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Laplace Transform Definition:\n",
      "ℒ{f(t)} = F(s) = ∫₀^∞ e^(-st) f(t) dt\n",
      "\n",
      "Common Laplace Transform Pairs:\n",
      "ℒ{u(t)} = ℒ{1} = 1/s\n",
      "ℒ{e^(-at)} = 1/(a + s)\n",
      "ℒ{sin(ωt)} = omega/(omega**2 + s**2)\n",
      "ℒ{cos(ωt)} = s/(omega**2 + s**2)\n",
      "ℒ{t²} = 2/s**3\n",
      "\n",
      "Symbolic Operations Examples:\n",
      "ℒ{3e^(-2t) + 4sin(3t)} = 12/(s**2 + 9) + 3/(s + 2)\n",
      "ℒ{u(t-1)e^(-2(t-1))} = exp(-s)/(s + 2)\n",
      "ℒ{e^(-3t)cos(2t)} = (s + 3)/((s + 3)**2 + 4)\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define symbols\n",
    "t, s = sp.symbols('t s', real=True)\n",
    "a, b, omega = sp.symbols('a b omega', real=True, positive=True)\n",
    "\n",
    "print(\"Laplace Transform Definition:\")\n",
    "print(\"ℒ{f(t)} = F(s) = ∫₀^∞ e^(-st) f(t) dt\")\n",
    "print()\n",
    "\n",
    "# Common Laplace transform pairs\n",
    "print(\"Common Laplace Transform Pairs:\")\n",
    "\n",
    "# Unit step function\n",
    "u = sp.Heaviside(t)\n",
    "laplace_u = sp.laplace_transform(u, t, s)\n",
    "print(f\"ℒ{{u(t)}} = ℒ{{1}} = {laplace_u[0]}\")\n",
    "\n",
    "# Exponential function\n",
    "exp_at = sp.exp(-a*t)\n",
    "laplace_exp = sp.laplace_transform(exp_at, t, s)\n",
    "print(f\"ℒ{{e^(-at)}} = {laplace_exp[0]}\")\n",
    "\n",
    "# Sine function\n",
    "sin_omega_t = sp.sin(omega*t)\n",
    "laplace_sin = sp.laplace_transform(sin_omega_t, t, s)\n",
    "print(f\"ℒ{{sin(ωt)}} = {laplace_sin[0]}\")\n",
    "\n",
    "# Cosine function\n",
    "cos_omega_t = sp.cos(omega*t)\n",
    "laplace_cos = sp.laplace_transform(cos_omega_t, t, s)\n",
    "print(f\"ℒ{{cos(ωt)}} = {laplace_cos[0]}\")\n",
    "\n",
    "# Power function\n",
    "t_n = t**2\n",
    "laplace_tn = sp.laplace_transform(t_n, t, s)\n",
    "print(f\"ℒ{{t²}} = {laplace_tn[0]}\")\n",
    "\n",
    "print(\"\\nSymbolic Operations Examples:\")\n",
    "\n",
    "# Linearity property\n",
    "f1 = 3*sp.exp(-2*t) + 4*sp.sin(3*t)\n",
    "F1 = sp.laplace_transform(f1, t, s)[0]\n",
    "print(f\"ℒ{{3e^(-2t) + 4sin(3t)}} = {F1}\")\n",
    "\n",
    "# Time shift property\n",
    "f2 = sp.Heaviside(t-1)*sp.exp(-2*(t-1))\n",
    "F2 = sp.laplace_transform(f2, t, s)[0]\n",
    "print(f\"ℒ{{u(t-1)e^(-2(t-1))}} = {F2}\")\n",
    "\n",
    "# Frequency shift property\n",
    "f3 = sp.exp(-3*t)*sp.cos(2*t)\n",
    "F3 = sp.laplace_transform(f3, t, s)[0]\n",
    "print(f\"ℒ{{e^(-3t)cos(2t)}} = {F3}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8988fc8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Numerical Examples:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ufo00\\AppData\\Local\\Temp\\ipykernel_31436\\1659964249.py:18: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.\n",
      "  integral = np.trapz(integrand, t_vals)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ufo00\\AppData\\Local\\Temp\\ipykernel_31436\\1659964249.py:52: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.\n",
      "  integral = np.trapz(integrand, t_vals)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Numerical evaluation of Laplace transforms\n",
    "print(\"\\nNumerical Examples:\")\n",
    "\n",
    "# Define time vector\n",
    "t_vals = np.linspace(0, 5, 1000)\n",
    "\n",
    "# Example 1: Exponential decay\n",
    "def f_exp(t):\n",
    "    return np.exp(-2*t)\n",
    "\n",
    "# Laplace transform at specific s values\n",
    "s_vals = np.linspace(0.1, 10, 100)\n",
    "F_exp_numerical = []\n",
    "\n",
    "for s_val in s_vals:\n",
    "    # Numerical integration using trapezoidal rule\n",
    "    integrand = np.exp(-s_val * t_vals) * f_exp(t_vals)\n",
    "    integral = np.trapz(integrand, t_vals)\n",
    "    F_exp_numerical.append(integral)\n",
    "\n",
    "# Analytical solution for comparison\n",
    "F_exp_analytical = 1 / (s_vals + 2)\n",
    "\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(t_vals, f_exp(t_vals), 'b-', linewidth=2)\n",
    "plt.xlabel('Time (t)')\n",
    "plt.ylabel('f(t)')\n",
    "plt.title('Original Function: f(t) = e^(-2t)')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(s_vals, F_exp_numerical, 'ro-', markersize=3, label='Numerical Integration')\n",
    "plt.plot(s_vals, F_exp_analytical, 'b-', linewidth=2, label='Analytical Solution')\n",
    "plt.xlabel('Frequency (s)')\n",
    "plt.ylabel('F(s)')\n",
    "plt.title('Laplace Transform: F(s) = 1/(s+2)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Example 2: Damped sinusoidal function\n",
    "def f_damped_sin(t):\n",
    "    return np.exp(-t) * np.sin(5*t)\n",
    "\n",
    "F_damped_sin_numerical = []\n",
    "for s_val in s_vals:\n",
    "    integrand = np.exp(-s_val * t_vals) * f_damped_sin(t_vals)\n",
    "    integral = np.trapz(integrand, t_vals)\n",
    "    F_damped_sin_numerical.append(integral)\n",
    "\n",
    "# Analytical solution: 5/((s+1)^2 + 25)\n",
    "F_damped_sin_analytical = 5 / ((s_vals + 1)**2 + 25)\n",
    "\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(t_vals, f_damped_sin(t_vals), 'b-', linewidth=2)\n",
    "plt.xlabel('Time (t)')\n",
    "plt.ylabel('f(t)')\n",
    "plt.title('Original Function: f(t) = e^(-t)sin(5t)')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(s_vals, F_damped_sin_numerical, 'ro-', markersize=3, label='Numerical Integration')\n",
    "plt.plot(s_vals, F_damped_sin_analytical, 'b-', linewidth=2, label='Analytical Solution')\n",
    "plt.xlabel('Frequency (s)')\n",
    "plt.ylabel('F(s)')\n",
    "plt.title('Laplace Transform: F(s) = 5/((s+1)² + 25)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
